Tag Archives: Linear algebra

December 21, 2010, 4:41 pm

Coming up in January

Fall Semester 2010 is in the books, and I’m heading into an extended holiday break with the family. Rather than not blog at all for the next couple of weeks, I’ll be posting (possibly auto-posting) some short items that take a look back at the semester just ended — it was a very eventful one from a teaching standpoint — and a look ahead and what’s coming up in 2011.

I’ll start with the look head to January 2011. We have a January term at my school, and thanks to my membership on the Promotion and Tenure Committee — which does all its review work during January — I’ve been exempt from teaching during Winter Term since 2006 when I was elected to the committee. This year I am on a subcommittee with only three files to review, so I have a relatively luxurious amount of time before Spring semester gets cranked up in February. A time, that is, which is immediately gobbled up by the…

Read More

May 23, 2010, 2:02 pm

Small proof of concept for inverted math classrooms

Geometric interpretation of the solution of a ...

Image via Wikipedia

The very last topic in the linear algebra class this semester (just concluded) unexpectedly gave me a chance to test-drive the inverted classroom model in a mathematics course, with pretty interesting results. The topic was least squares solutions and applications to linear models. I like to introduce this topic without lecture, since it’s really just an application of what they’ve learned about inner products and orthogonality. Two days are set aside for this topic. In the first day, I gave this group activity:

[scribd id=31814651 key=key-u9ax6c6fhdh5684hkle mode=list]

The intent was to get this activity done in about 35 minutes and then talk about the normal equations — a much faster way of finding the least-squares solution than what this activity entails — afterwards. Then I meant …

Read More

May 15, 2010, 11:41 am

The semester in review

Plot of the vector field f(x,y) = (-y,x).

Image via Wikipedia

I’ve made it to the end of another semester. Classes ended on Friday, and we have final exams this coming week. It’s been a long and full semester, as you can see by the relative lack of posting going on here since around October. How did things go?

Well, first of all I had a record course load this time around — four different courses, one of which was the MATLAB course that was brand new and outside my main discipline; plus an independent study that was more like an undergraduate research project, and so it required almost as much prep time from me as a regular course.

The Functions and Models class (formerly known as Pre-calculus) has been one of my favorites to teach here, and this class was no exception. We do precalculus a bit differently here, focusing on using functions as data modeling …

Read More

March 21, 2010, 7:32 pm

Calculus reform's next wave

There’s a discussion going on right now in the Project NExT email list about calculus textbooks, the merits/demerits of the Stewart Calculus textbook, and where — if anywhere — the “next wave” of calculus reform is going to come from. I wrote the following post to the group, and I thought it would serve double-duty fairly well as a blog post. So… here it is:


I’d like to add my $0.02 worth to this discussion just because (1) I’m a longtime Stewart Calculus user, having used the first edition (!) when I was an undergrad and having taught out of it for my entire career, and (2) I’m also a fairly consistent critic of Stewart’s calculus and of textbooks in general.

I try to see textbooks from the viewpoints of my students. From that vantage point, I unfortunately find very little to say in favor of Stewart’s franchise of  books, including the current edition, all of the…

Read More

March 12, 2010, 7:38 am

ICTCM underway

It’s a beautiful day here on the shores of Lake Michigan as the ICTCM gets underway. It’s a busy day and — to my never-ending annoyance — there is no wireless internet in the hotel. So I won’t be blogging/tweeting as much as I’d like. But here’s my schedule for the day.

  • 8:30 – Keynote address.
  • 9:30 – Exhibits and final preparations for my 11:30 talk.
  • 10:30 – “Developing Online Video Lectures for Online and Hybrid Algebra Courses”, talk by Scott Franklin of Natural Blogarithms.
  • 11:10 – “Conjecturing with GeoGebra Animations”, talk by Garry Johns and Tom Zerger.
  • 11:30 – My talk on using spreadsheets, Winplot, and Wolfram|Alpha|Alpha in a liberal arts calculus class, with my colleague Justin Gash.
  • 12:30 – My “solo” talk on teaching MATLAB to a general audience.
  • 12:50 – “Programming for Understanding: A Case Study in Linear Algebra”, talk by Daniel Jordan.
  • 1:30 – “Over a Decade of…

Read More

February 27, 2010, 6:32 am

Is Khan Academy the future of education?

Salman Khan is a former financial analyst who quit his day job so that he could form Khan Academy — a venture in which he makes instructional videos on mathematics topics and puts them on YouTube. And he has certainly done a prolific job of it — to the tune of over a thousand short videos on topics ranging from basic addition to differential equations and also physics, biology, and finance.  Amazingly, he does this all on his own time, in a remodeled closet in his house, for free:

I can attest to the quality of his linear algebra videos, some of which I’ve embedded on the Moodle site for my linear algebra course. They are simple without being dumbed down, and what he says about the 10-minute time span in the PBS story is exactly right — it’s just the right length for a single topic.

What do you think about this? What role do well-produced, short, simple, free video…

Read More